{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns\n",
    "from ERANataf import ERANataf\n",
    "from ERADist import ERADist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Cross Entropy for Bayesian updating\n",
    "Comments \n",
    "W :  Importance weights of the Cross Entropy method W = phi/h\n",
    "W_t : Importance weights of the improved Cross Entropy W_t = L**beta*W\n",
    "----------------------------------------------------------------\n",
    "Input\n",
    "* N         : number of samples per level\n",
    "* L_fun     : limit state function\n",
    "* max_it    : maximum number of iterations\n",
    "* Prior     : Nataf distribution object or marginal distribution\n",
    "* CV_target :  target Coefficient of vairation of weights\n",
    "----------------------------------------------------------------\n",
    "Output\n",
    "* Z         : normalisation constant\n",
    "* lv        : total number of levels\n",
    "* N_tot     : total number of samples\n",
    "* samplesU  : object with the samples in the standard nromal space\n",
    "* samplesX  : object with the samples in the original space\n",
    "* beta_t    : intermediate tempering value\n",
    "\"\"\"\n",
    "def CEUP_SG(N,L_fun, prior, max_it,CV_target):\n",
    "#     # initial check if there exists a Nataf object\n",
    "#     if isinstance(prior, ERANataf):  # use Nataf transform (dependence)\n",
    "#         dim = len(prior.Marginals)  # number of random variables (dimension)\n",
    "#         u2x = lambda u: prior.U2X(u)  # from u to x\n",
    "\n",
    "#     elif isinstance(prior, ERADist):  # use distribution information for the transformation (independence)\n",
    "#         # Here we are assuming that all the parameters have the same distribution !!!\n",
    "#         # Adjust accordingly otherwise\n",
    "#         dim = 1  # number of random variables (dimension)\n",
    "#         u2x = lambda u:prior.icdf(sp.stats.norm.cdf(u))  # from u to x\n",
    "    dim = 1\n",
    "    x2u = lambda x: (x-prior.mean())/prior.std()\n",
    "    u2x = lambda u: prior.mean()+prior.std()*u\n",
    "    L_transformed = lambda u: Likelihood(u2x(u))\n",
    "    N_tot = 0\n",
    "    mu_init = np.zeros(dim)\n",
    "    si_init = np.identity(dim)\n",
    "    beta_t = np.zeros(max_it)\n",
    "    samplesU = list()\n",
    "    # CE procedure\n",
    "    mu_U = mu_init\n",
    "    si_U = si_init\n",
    "    # Iteration\n",
    "    for t in range(max_it):\n",
    "        # Generate samples and save them\n",
    "        U = sp.stats.multivariate_normal.rvs(mean=mu_U,cov=si_U,size=N).reshape(-1,dim)\n",
    "        samplesU.append(U.T)\n",
    "\n",
    "        # Evaluate the likelihood function\n",
    "        Leval = L_transformed(U)\n",
    "        # Initialize beta, beta increases from 0 to 1\n",
    "        if t==0 :\n",
    "            beta_t[t] = 0\n",
    "        else:\n",
    "            beta_t[t] = beta_new\n",
    "\n",
    "        # calculatiing h for the likelihood weight\n",
    "        h = sp.stats.multivariate_normal.pdf(U,mu_U,si_U)\n",
    "        phi = sp.stats.multivariate_normal.pdf(U,mean=np.zeros(dim),cov = np.identity(dim))\n",
    "        W = phi/h\n",
    "        if beta_t[t] >= 1-1e-6:\n",
    "            break\n",
    "        # Count generated samples\n",
    "        N_tot += N\n",
    "        \n",
    "        Wt_fun = lambda beta: W*np.power(Leval,beta)[:,0]\n",
    "        CV_Wt_fun = lambda beta: np.std(Wt_fun(beta))/np.mean(Wt_fun(beta))\n",
    "        ESS_target = N/(1+CV_target**2)\n",
    "        ESS_observed = lambda beta: N/(1+(CV_Wt_fun(beta))**2)\n",
    "        fmin = lambda beta: abs(ESS_target-ESS_observed(beta))\n",
    "        beta_new = sp.optimize.fminbound(fmin,beta_t[t],1)\n",
    "        # Update W_t\n",
    "        W_t = Wt_fun(beta_new)\n",
    "        delta_Wt = np.std(W_t)/np.mean(W_t)\n",
    "        # Parameter update: closed form\n",
    "        mu_U = W_t@U/sum(W_t)\n",
    "        Xtmp = U-mu_U\n",
    "        Xo = Xtmp *np.tile(np.sqrt(W_t),(dim,1)).T\n",
    "        Si_U = np.matmul(Xo.T,Xo)/np.sum(W_t)+1e-6*np.identity(dim) \n",
    "    # total levels\n",
    "    lv = t\n",
    "    # Calculate the integral of the posterior Integral = sum(W_t)/N\n",
    "    Z = sum(W_t)/N\n",
    "    # Transform the samples to the physical/ original space\n",
    "    samplesX = list()\n",
    "    for i in range(lv):\n",
    "        samplesX.append(u2x(samplesU[i]))\n",
    "    return Z,lv,N_tot,samplesU,samplesX,beta_t \n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Parameter definition\n",
    "# Fixed parameters\n",
    "m = 3.5\n",
    "C = np.exp(-1.5667*m - 27.5166)\n",
    "a_0 = 0.10\n",
    "t = 50 # lifetime\n",
    "mu_DS , sigma_DS = 60,10\n",
    "a = lambda DS: ((1-m/2)*C*DS**m*(np.pi)**(m/2)*10**5 * t + a_0**(1-m/2))**((1-m/2)**(-1))\n",
    "prior = lambda DS: sp.stats.norm.pdf(DS,loc = mu_DS,scale=sigma_DS)\n",
    "dist_prior = ERADist(\"Normal\",\"MOM\",[mu_DS,sigma_DS])\n",
    "# Likelihood function\n",
    "a_star = a(70)\n",
    "a_tilde = np.random.normal(a_star, 0.01, 10)\n",
    "def Likelihood(DS):\n",
    "    total_likelihood = 1\n",
    "    for i in range(a_tilde.size):\n",
    "        total_likelihood = total_likelihood * sp.stats.norm.pdf(a(DS) - a_tilde[i], loc=0, scale =0.01)\n",
    "    return total_likelihood\n",
    "def target_dist(DS):\n",
    "    return prior(DS)*Likelihood(DS)\n",
    "N = 1000\n",
    "max_it = 50\n",
    "CV_target = 1.5\n",
    "dim = 1\n",
    "# Method 2 numerical integration of the denominator\n",
    "# constant = sp.integrate.quad(target_dist,-np.inf,np.inf)\n",
    "constant = sp.integrate.quad(target_dist,0,100)\n",
    "\n",
    "[Z,lv,N_tot,samplesU,samplesX,beta_t] = CEUP_SG(N,Likelihood,dist_prior,max_it,CV_target)\n",
    "# Plot samples \n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesU[0],label='beta=0')\n",
    "    for sample in samplesU[1:-1]:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesU[-1],label='beta=1')\n",
    "    plt.xlabel('u')\n",
    "    plt.ylabel('target_dist')\n",
    "    plt.title('Intermediate target distribution in tranformed space')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesX[0],label='beta=0')\n",
    "    for sample in samplesX[1:-1]:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesX[-1],label='beta=1')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('target_dist')\n",
    "    plt.title('Intermediate target distribution in physical space')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(66972368635665.375, 6602.019867305537)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constant = sp.integrate.quad(target_dist,0,100)\n",
    "constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "68520026504734.78"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\wanch\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in power\n",
      "  \n",
      "C:\\Users\\wanch\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in power\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2092f8c4148>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot of the prior likelihood and analytical and numerical posterior\n",
    "DS = np.arange(-20,20)\n",
    "plt.plot(DS,prior(DS),'-+',label='prior')\n",
    "plt.plot(DS,Likelihood(DS),'-*',label='Likelihood')\n",
    "plt.plot(DS,target_dist(DS)/constant[0],'-x',label='posterior_numerical')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2092f2eaa88>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot of the prior likelihood and analytical and numerical posterior\n",
    "DS = np.arange(0,100)\n",
    "#plt.plot(DS,prior(DS),'-+',label='prior')\n",
    "#plt.plot(DS,Likelihood(DS),'-*',label='Likelihood')\n",
    "plt.plot(DS,target_dist(DS)/constant[0],'-x',label='posterior_numerical')\n",
    "sns.distplot(samplesX[-1],label='posterial_CE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
